The first case considers a hanging filament of length \(L=1\)  m without an ambient fluid (in order to independently test the solid solver alone), as proposed by [1]}. Adopting the same arbitrary units, the filament is initially held stationary at an angle \(k=0.1\pi \)  radians from the vertical, where the physical parameters correspond to a Froude number \(Fr = v/\sqrt{gL} = 10.0\)  (\(g\)  is the gravitation constant) and a bending rigidity \(EI=0.01\)  Pa m\(^3\) . Snapshots of the simulated positions of the filament over a time period of 0.8 s are illustrated in Figure REF , where a spatial discretization of \(N = 100\)  elements is utilized together with a timestep of \(\Delta t = 0.0001\)  s. Again, the solutions produced by the solver of this work are in excellent agreement with those results presented by [1]}.
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